**Improve School Math**

– Transition to Algebra (Recommended for 4th, 5th and 6th Graders)

– Algebra-1 and Integrated Math-1 (Recommended for 8th and 9th Graders and advanced 7th Graders)

– Algebra-2 (Recommended for 10th graders and advanced 8th and 9th graders)

# Summer Math Camp

### You can apply for our 2020 Summer Camps Now and benefit from Super Early Bird Discounts!

**Courses to be offered in 2020 Summer Math Camps**

**Go Beyond!**

– Advanced Middle School Math with MathCounts/AMC 8-10 Problems (Recommended for advanced 6th, 7th and 8th Graders)

– Advanced High School Math with AMC 10/12 Problems (Recommended for advanced 9th, 10th and 11th Graders)

– Proof Mathematics with AIME Problems

### This page will be updated for 2020 Summer Camps!

CyberMath Academy offered a math camp at two locations in the summer of 2019:

**Dates:** July 6– 17, 2019 (see calendar below for details please)

**Location:** Classes will be held at Harvard Law School, Wasserstein Hall, 1585 Massachusetts Ave, Cambridge, MA 02138.

Residential Students will stay at Harvard Square.

**Ages:** 11-18 for residential students, 9-18 for day students.

**Tuition:** $1,985 for day campers, $4,700 for residential students.

Please scroll down for more information.

**Master Math in an Intensive Camp This Summer!**

CyberMath Academy’s **Summer Math Camp** in Boston, MA is a selective summer program for students who would like to sharpen their math skills in the inspiring and motivating atmosphere of an Ivy League College. Our math camp provides a challenging environment in summer for students in which they master mathematics with the participation of brilliant students from all over the globe.

**Advanced Math Program – Designed by Justin Stevens**

“- Author of Olympiad Number Theory Through Challenging Problems Book

– “Our teacher, Justin, was a legend.” 2018 Camp Participant

– “Justin is a crazy good teacher and understands kids.” 2018 Camp Participant

– “Justin is the most awesome teacher EVER!!!’ 2018 Camp Participant”

“Math Olympiad Program – Designed by Evan Chen

– One of the coaches of the USA IMO Team

– Co-Exam Coordinator for the USA Olympiad Team Selection Tests

– Assistant Academic Director of the Math Olympiad Summer Program (MOP)

– Member of the USA Math Olympiad (USAMO) Committee”

**Courses to Choose From and Who The Summer Math Camp is For**

**1- Students who would like to excel in school mathematics**

Courses to choose from:

###### Advanced Middle School Math with MathCounts/AMC 8-10 Problems

*This course covers the main topics in middle school math. Students will be mastering these topics while solving challenging problems at the level of or from MathCounts, AMC-8, AMC 10 and similar competitions. Students go above and beyond Common Core standards in this brain-stimulating course. Students will also solve mathematical puzzles and cyphers in our summer math camp and learn topics that are typically not covered at traditional school settings.***Recommended Grade Levels:**Although we do not limit students by grade level in our summer math camps, this course is typically recommended for students in grades 4th-8th.**Course Description:**This course will familiarize students with the essential concepts and techniques in Pre-Algebra, Algebra I, Geometry, Number Theory and Combinatorics. We will have a specific emphasis on problem solving where the students will constantly be challenged to think creatively.**Contest Preparation:**MathCounts, AMC 8, AMC 10.**Course Objectives:**As of the completion of the summer math camp, students will:1. Have complete mastery of concepts covered in standard Pre-Algebra, Algebra I and Geometry courses, as well as topics not covered in traditional school curriculum.

2. Be able to explain and employ important theorems and techniques used in Combinatorics, Number Theory, and Geometry.

3. Be able to reduce unfamiliar problems to basic principles, and cleverly employ techniques they’ve learned to find shortcuts in solution methods.

**Teaching Philosophy:**We believe that building good problem-solving skills is as (if not more) important than knowing lots of theorems. As such, although the course will cover a considerable amount of material, the main emphasis will be on building problem-solving intuition and training students to think creatively when faced with classes of problems they’ve never seen before.**Class Participation:**Students are expected to actively participate in class. We will employ the Socrates method, which is a cooperative dialogue between the students and teacher to stimulate critical thinking. Students will also collaborate with classmates while solving challenging problems.**Curriculum:**The course curriculum is owned and copyright by CyberMath Academy. The class material is composed of unique blends of problems hand picked from prestigious competitions from around the globe, along with many historical problems and fascinating puzzles.**Algebra**• Ratios and Proportions

• Algebraic Expressions

• Linear Equations

• Functions

• Inequalities

• Polynomial Expressions

• Pascal’s Triangle

• Binomial Theorem

• Quadratic Equations**Combinatorics**• Counting

• Statistics

• Probability

• Permutations

• Combinations**Number Theory**• Divisibility

• GCD and LCM

• Prime Factorization

• Radicals and Exponents

• Modular Arithmetic

• Sequences and Series

• Gauss’s Formula**Geometry**• Angles

• Triangles

• Pythagorean Theorem

• Polygons

• Circles

• Perimeter, Area and Volume

• Coordinate Geometry

• 3D Geometry

###### Advanced High School Math with AMC 10/12 Problems

*This course prepares students for American Mathematics Competitions 10 and 12 and the non-proof parts of AIME. The topics taught include***the entire high school curriculum including trigonometry, advanced algebra, precalculus and advanced geometry,**but exclude calculus. Our curriculum also includes some additional challenging and brain-stimulating topics outside of the traditional school curriculum.**Recommended Grade Levels:**Although we do not limit students by grade level in our summer math camps, this course is typically recommended for advanced 7th and 8th graders and high school students.**Course Description:**This course will familiarize students with the essential concepts and techniques in Algebra II, PreCalculus, Combinatorics, Number Theory, and Geometry. We will have a specific emphasis on problem solving where the students will constantly be challenged to think creatively.**Contest Preparation:**AMC 10/12, AIME, ARML, Mandelbrot, Purple Comet.**Course Objectives:**As of the completion of the summer math camp, students will:1. Have complete mastery of concepts covered in standard Algebra II and PreCalculus courses, as well as more advanced topics (such as Vieta’s formulas, Complex Numbers, and manipulation of Series).

2. Be able to explain and employ important theorems and techniques used in Combinatorics, Number Theory, and Geometry.

3. Be able to reduce unfamiliar problems to basic principles, and cleverly employ techniques they’ve learned to find shortcuts in solution methods.

**Teaching Philosophy:**We believe that building good problem-solving skills is as (if not more) important than knowing lots of theorems. As such, although the course will cover a considerable amount of material, the main emphasis will be on building problem-solving intuition and training students to think creatively when faced with classes of problems they’ve never seen before.**Class Participation:**Students are expected to actively participate in class. We will employ the Socrates method, which is a cooperative dialogue between the students and teacher to stimulate critical thinking. Students will also collaborate with classmates while solving challenging problems.**Curriculum:**The course curriculum is owned and copyright by CyberMath Academy. The class material is composed of unique blends of problems hand picked from prestigious competitions from around the globe, along with many historical problems and fascinating puzzles.**Topics Covered In This Course****Algebra**– Quadratics/Discriminants & Conic Sections

– System of Equations

– Polynomial Division

– Rational Root Theorem

– Fundamental Theorem of Algebra

– Vieta’s Formulas

– Sequences and Series

– Induction

– Radicals and Rationalizing Denominators

– Algebraic Factorizations

– Complex Numbers

– Inequalities

– Functions

– Exponents and Logarithms**Combinatorics**– Basic Counting: Constructive and Complimentary

– Sets, Bijections, and Logic

– Principle of Inclusion Exclusion

– Combinations and Permutations

– Pascal’s Triangle

– Binomial Theorem

– Combinatorial Identities

– Pigeonhole Principle

– Expected Value

– Stars & Bars

– Recursion

– Fibonacci Numbers**Number Theory**– Prime Factorization

– Divisibility Rules

– Euclidean Algorithm

– Diophantine Equations

– Bezout’s Identity

– Modular Arithmetic & Exponentiation

– Fermat’s Little Theorem

– Wilson’s Theorem

– Chinese Remainder Theorem

– Multiplicative Functions

– Euler’s Theorem**Geometry**– Congruent & Similar Triangles

– Special Parts of a Triangle

– Triangle Area Formulas

– Quadrilaterals

– Angles in Polygons

– Inscribed Angles in Circles

– Power of a Point

– Three-Dimensional Geometry

– Trigonometry for Right Triangles

– Unit Circle & Radians

– Trigonometric Identities

– Extended Law of Sines & Law of Cosines

– Polar Coordinates & Geometry of Complex Numbers**Click below to see sample lecture notes****AUTHORS****Justin Stevens:**Accelerated Math Program Coordinator

University of Alberta – jstevens@cybermath.academy – (909) 713-4398**Forest Kobayashi:**Curriculum Designer, Harvey Mudd College**Alex Toller:**Curriculum Designer

If you would like to get more information on AMC 8, 10, 12 and AIME competitions, please visit Mathematical Association of America’s American Mathematics Competitions (AMC) Page.

**2- Students who would like to go above and beyond school mathematics**

Courses to choose from:

– Proof Mathematics with AIME Problems

This course is a part of our Math Olympiad Program. You can find more information about our Math Olympiad Program below.

###### Math Olympiad Program Levels

To find out what course is best for you at our summer math camp, please look at the information below:

There are two tracks in this course:

**Proof Mathematics with AIME Problems**For students who can comfortably qualify for the

AIME and solve the first half of problems on the exam. These students might be

aiming to qualify for USA(J)MO and have a pleasant start on the olympiad.**USA(J)MO:**For students who can already comfortably qualify for USA(J)MO, and

are aiming to score highly on it.**First: Please determine your level below**(1) Starting out on AMC, trying to qualify for AIME

(2) Can solve 2 problems on AIME, hoping to solve 8

(3) Can solve 6+ problems on AIME, hoping to solve 13

(4) Can qualify for USA(J)MO, hoping to solve a problem or two

(5) Can solve one or two USA(J)MO problems and solve hard USAJMO or medium USAMO problems

(6) Aiming to solve the final P3 / P6 problems on USAMO

**Second:Learn about the tracks in our Math Olympiad Program**Our Math Olympiad Program has two tracks:

*Entry Level Math Olympiad Course with Computations (Advanced AIME with Proofs)** Prerequisites: 6+ on AIME

* Aiming for high AIME scores, and a couple problems on USA(J)MO

*Advanced Math Olympiad Course (USAJMO)** Prerequisites: consistently qualify for USA(J)MO

* Aiming to score 14+ on USAMO

**Third: Placement**– If you are in levels 1 or 2, you should sign up for our Advanced High School Math with AMC 10/12 Problems course. It covers AMC 10/12 and the non-proof problems on AIME.

– If you are in levels 3 or 4, you should sign up for our Advanced AIME with Proofs course.

– If you are in levels 5 or 6, you should sign up for our USA(J)MO course.

Have questions? E-mail our Math Olympiad Program Coordinator Evan Chen at echen@cybermath.academy

###### Math Olympiad Program Curriculum

There are two tracks in this program:

**Advanced AIME with Proofs:**For students who can comfortably qualify for the

AIME and solve the first half of problems on the exam. These students might be

aiming to qualify for USA(J)MO and have a pleasant start on the olympiad.**USA(J)MO:**For students who can already comfortably qualify for USA(J)MO, and

are aiming to score highly on it.These two tracks overlap in any given year. The curriculum runs in a three-year cycle.

**Contest preparation:**AIME, HMMT, USA(J)MO, IMO.**Curriculum:**The course operates on a three-year cycle, so students can repeat the course up to three times total, across both tracks. The summer math camp and year-round materials are disjoint.A detailed listing of topics covered appears below. Not all topics occur in all years. Most topics occur in multiple years, but they will have different examples and problems each time they appear over the three-year cycle.

Each iteration of the course contains several practice exams.

**1- Topics appearing only in Advanced AIME with Proofs****Algebra***Symmetric Polynomials.*Vieta’s formulas, Newton sums, fundamental theorem of elementary symmetric polynomials.*Logarithms.*Computational problems and equations involving logarithms.*Trig Equation.*Algebraic problems involving trig functions.*Intro Functional Equation.*Introduction to olympiad-style functional equations. Substitutions, injectivity and surjectivity, Cauchy’s functional equation.*Inequalities.*Introduction to olympiad-style inequalities. AM-GM and Cauchy-Schwarz.

**Combinatorics***Computations with Probability.*Random variables, expected value, linearity of expectation.*Enumeration.*Computational counting problems.- Monovariants and Invariants.
*Finite processes.*

*Computational Geometry.*AIME-style problems in Euclidean geometry.

Angle Chasing.*Trig in Geometry.**Elementary Geometry.*Angle chasing, power of a point, homothety.*Basics of Complex Numbers. Introduction to complex numbers in geometry.*

**Number theory***Computations with Modular Arithmetic.*Fermat, Wilson, Chinese Remainder theorem.*Diophantine Equations.*Introduction to olympiad-style Diophantine equations.*Chinese Remainder Theorem.*

**2- Topics appearing in both tracks****Algebra***Generating Functions.*Their uses in combinatorial sums.*Linear Recursions and Finite Differences.**Sums.*Swapping order of summation.*Polynomials.*Fundamental theorem of algebra, factorizations, roots.

**Combinatorics***Weights and Colorings.**Induction and Recursion.**Linearity of Expectation and Double-Counting.**Algorithms.*Combinatorial problems involving discrete-time processes.*Graph Theory.*Definitions and problems.*Ad-Hoc Constructions.**Problems on Rectangular Grids.*

**Geometry***Power of a Point.**Homothety**Common Congurations.*

**Number theory***Divisibility and Euclidean Algorithm.*Bounding the remainders.*Look at the Exponent.*p-adic evaluation, lifting the exponent.*Orders. Primes of the form a2 + b2.*Primitive roots.

**3- Topics appearing only in USA(J)MO****Algebra***Functional Equations.*More diffi cult functional equations at the USAMO/IMO level.*Advanced Inequalities.*Jensen and Schur. Fudging, smoothing.*Analysis and Calculus.*Understanding the complete theorem statements in calculus and how they can be applied to olympiad problems. Differentiation and the relation

to multiplicity of roots. Lagrange multipliers. Compactness.

**Combinatorics***Advanced Graph Theory.*More di fficult olympiad problems involving graphs.*Advanced Algorithms.**Games and Processes.*

**Geometry***Projective Geometry.*Harmonic bundles, poles and polars.*Inversion.**Spiral Similarity.**Complex Numbers.*Applications to problems.*Barycentric Coordinates.*Applications to problems.

**Number theory***Constructions in Number Theory.**Integer Polynomials.*Irreducibility, minimal polynomials, a taste of Galois theory.*Quadratic Reciprocity.*Legendre symbols.

**Distribution of Math Strands**

**Morning Sessions:** Combinatorics and Geometry topics will be covered.

**Afternoon Sessions:** Algebra and Number Theory topics will be covered.

**Outstanding Teachers!**

Please see our faculty page for our instructors. Summer Math Camp instructors will be some of the instructors listed on our faculty page or other outstanding teachers with similar credentials.

**Guest Lectures by Harvard, MIT Researchers**

TBA.

The guest lectures will be held at the 250-year old courtroom on the first day of the camp.

**Students’ Forum**

There will be two student forums for our students:

**Students’ Forum 1:** Learn how to get accepted to top colleges from students who currently attend Harvard, MIT and other top colleges.

**Students’ Forum 2:** Learn how to prepare for math competitions and olympiads from champions who aced these tests.

**Harvard, MIT Campus Tours and Lab Visits**

Harvard and MIT Campus Tours and laboratory visits are scheduled each year.

**Sightseeing**

We will visit the historical places to see first-hand where the United States was founded and learn about its history. Walk along The Freedom Trail, try many tastes at Quincy Market, when tired of walking hop on a Duck Tour and take a walk along Charles River. Feel smarter (pronounced SMAHTAH) at Harvard Square.

**Schedule of Activities**

Date | Morning | Afternoon |
---|---|---|

Fri, July 5 | Residential and Int. Students Arrive | Orientation, Time at Harvard Square |

Sat, July 6 | Opening,Placement Tests & Guest Lecture | Math Classes |

Sun, July 7 | Math Classes | Math Classes |

Mon, July 8 | Math Classes | Math Classes |

Tue, July 9 | Math Classes | Math Classes |

Wed, July 10 | Math Classes | Math Classes |

Thu, July 11 | Harvard Campus Tour, Students’ Forum | MIT Campus Tour |

Fri, July 12 | Math Classes | Math Classes |

Sat, July 13 | Math Classes | Math Classes |

Sun, July 14 | Math Classes | Math Classes |

Mon, July 15 | Math Classes | Math Classes |

Tue, July 16 | Math Classes | Math Classes |

Wed, July 17 | Math Classes | Practice Test, Award Ceremony |

Domestic Residential Students Depart | ||

Thu, July 18 | Academic Counseling for Int. Students | Study Planning for Int. Students |

Fri, July 19 | International Students Depart | |

**Optional Additional East Coast Trip**

This optional program is a wonderful opportunity for students who would like to have an eye-opening and awe-inspiring experience visiting the top academic and touristic destinations in the East Coast of the United States. Many international students as well as domestic ones would like to breathe the motivating air in these world renowned places and experience first-hand what makes them great. Please note that this is an optional program in addition to our regular summer camp program and requires an additional fee of $3,850. This fee covers everything including transportation, meals, accommodation, applicable entrance fees for museums and other attractions.

Date | Morning | Afternoon |
---|---|---|

Fri, July 19 | Harvard Admissions Information, Scientists’ Forum | MIT & Kendall Square Labs Tour |

Sat, July 20 | Greater Boston Area Tour | Greater Boston Area Boat Tour |

Sun, July 21 | Yale University Campus Tour | Yale University Admissions Session |

Mon, July 22 | New York City Tour | New York City Boat Tour |

Tue, July 23 | American Museum of Natural History, The Metropolitan Museum of Art | Columbia University Tour |

Wed, July 24 | Shopping Mall: Outlet Stores | Students Depart |

**Daily Schedule**

Time | Activity | Notes |
---|---|---|

7:15 am – 8:15 am | Breakfast | Residential Students Only |

8:15 am – 8:45 am | Day students arrive | |

9:00 am – 12:15 pm | Morning classes | |

12:15 pm – 1:15 pm | Lunch and Activity time | Conversation with teachers/counselors |

1:15 pm – 4:30 pm | Afternoon classes | |

4:30 pm – 5:00 pm | Day students depart | |

5:00 pm – 6:00 pm | Free time | Residential Students Only* |

6:00 pm – 7:15 pm | Dinner | Residential Students Only* |

7:30 pm – 9:30 pm | Study Time | Residential Students Only* |

9:30 pm – 10:30 pm | Free Time | Residential Students Only |

10:45 pm | Lights Out | Residential Students Only |

*Day students who wish to attend supervised evening recreational and academic activities at the residential program may do so for an additional fee. The cost will be $200 (including dinner and all activities).

**Transportation to Summer Math Camp**

**Bus Service for Day Students**

We offer bus transportation to our camp site if enough number of students sign up for our Summer Math Camp as day students from the cities listed below. Extra charge will apply and space is limited.

For day students, we provide buses from the following cities: Acton, Lexington, Weston, and Newton

**Airport Pickup**

Domestic residential and international students who will be staying with us overnight at our summer math camp are expected to arrive at Boston Logan International Airport or at the camp site between 7 am – 7 pm on July 5th. For tuition and fees, please see below.

**Summer Math Camp Tuition and Deadlines**

Tuition Type | Deadline | Day Student | Residential Student |
---|---|---|---|

Super Early Bird | November 1st | $1,650 | $3,910 |

Early Registration | April 1st | $1,885 | $4,450 |

Regular Registration | June 1st | $1,985 | $4,700 |

Late Registration | July 14th | $2,085 | $4,950 |

Residential Tuition covers classes & teaching materials, activities, accommodation, meals and in-camp transportation.

**Fees**

International Students’ Fee: Additional $585.

Airport Pickup/Dropoff fee: $60 each

Lunch Fee for Day Students: $232 (Day Students might choose to bring their own lunch or purchase lunch at the University.)

Optional East Coast / Silicon Valley Program Fee: $3,850

**You can save up to $790 by registering early!**

**Summer Math Camp Details**

**Dates:** July 15–27, 2019 (see calendar below for details please)

**Location:** Classes will be held at **Stanford University** in Stanford, CA

Residential Students will stay in Silicon Valley.

**Ages:** 11-18 for residential students, 9-18 for day students.

**Tuition:** $1,985 for day campers, $4,700 for residential students.

Please scroll down for more information.

**Master Math in an Intensive Camp This Summer!**

CyberMath Academy’s **Summer Math Camp** in Silicon Valley is a selective summer program for students who would like to sharpen their math skills in the inspiring and motivating atmosphere of an Ivy League College. Our math camp provides a challenging environment in summer for students in which they master mathematics with the participation of brilliant students from all over the globe.

**Dates**

July 15–27, 2019 (see calendar below for details please)

**Classes will be held at: Stanford University**

**Students will stay in: Silicon Valley**

**Guest Lectures by Stanford Researchers**

TBA.

**Students’ Forum**

Learn how to get accepted to top colleges from students who currently attend Stanford and other top colleges.

**Stanford Campus Tour**

Stanford Campus Tours and laboratory visits are scheduled each year.

We will also see the beautiful San Francisco Bay Area. Our San Francisco tour includes Twin Peaks, Fisherman’s Wharf, Pier 39, Treasure Island, Golden Gate Bridge, Coit Tower and the yummy yummy Ghirardelli Chocolate Factory.

**Advanced Math Program – Designed by Justin Stevens**

“- Author of Olympiad Number Theory Through Challenging Problems Book

– “Our teacher, Justin, was a legend.” 2018 Camp Participant

– “Justin is a crazy good teacher and understands kids.” 2018 Camp Participant

– “Justin is the most awesome teacher EVER!!!’ 2018 Camp Participant”

**Math Olympiad Program – Designed by Evan Chen**

“- One of the coaches of the USA IMO Team

– Co-Exam Coordinator for the USA Olympiad Team Selection Tests

– Assistant Academic Director of the Math Olympiad Summer Program (MOP)

– Member of the USA Math Olympiad (USAMO) Committee”

**Courses to Choose From and Who The Summer Math Camp is For**

**1- Students who would like to excel in school mathematics**

Courses to choose from:

###### Advanced Middle School Math with MathCounts/AMC 8-10 Problems

*This course covers the main topics in middle school math. Students will be mastering these topics while solving challenging problems at the level of or from MathCounts, AMC-8, AMC 10 and similar competitions. Students go above and beyond Common Core standards in this brain-stimulating course. Students will also solve mathematical puzzles and cyphers in our summer math camp and learn topics that are typically not covered at traditional school settings.***Recommended Grade Levels:**Although we do not limit students by grade level in our summer math camps, this course is typically recommended for students in grades 4th-8th.**Course Description:**This course will familiarize students with the essential concepts and techniques in Pre-Algebra, Algebra I, Geometry, Number Theory and Combinatorics. We will have a specific emphasis on problem solving where the students will constantly be challenged to think creatively.**Contest Preparation:**MathCounts, AMC 8, AMC 10.**Course Objectives:**As of the completion of the summer math camp, students will:1. Have complete mastery of concepts covered in standard Pre-Algebra, Algebra I and Geometry courses, as well as topics not covered in traditional school curriculum.

2. Be able to explain and employ important theorems and techniques used in Combinatorics, Number Theory, and Geometry.

3. Be able to reduce unfamiliar problems to basic principles, and cleverly employ techniques they’ve learned to find shortcuts in solution methods.

**Teaching Philosophy:**We believe that building good problem-solving skills is as (if not more) important than knowing lots of theorems. As such, although the course will cover a considerable amount of material, the main emphasis will be on building problem-solving intuition and training students to think creatively when faced with classes of problems they’ve never seen before.**Class Participation:**Students are expected to actively participate in class. We will employ the Socrates method, which is a cooperative dialogue between the students and teacher to stimulate critical thinking. Students will also collaborate with classmates while solving challenging problems.**Curriculum:**The course curriculum is owned and copyright by CyberMath Academy. The class material is composed of unique blends of problems hand picked from prestigious competitions from around the globe, along with many historical problems and fascinating puzzles.**Algebra**• Ratios and Proportions

• Algebraic Expressions

• Linear Equations

• Functions

• Inequalities

• Polynomial Expressions

• Pascal’s Triangle

• Binomial Theorem

• Quadratic Equations**Combinatorics**• Counting

• Statistics

• Probability

• Permutations

• Combinations**Number Theory**• Divisibility

• GCD and LCM

• Prime Factorization

• Radicals and Exponents

• Modular Arithmetic

• Sequences and Series

• Gauss’s Formula**Geometry**• Angles

• Triangles

• Pythagorean Theorem

• Polygons

• Circles

• Perimeter, Area and Volume

• Coordinate Geometry

• 3D Geometry

###### Advanced High School Math with AMC 10/12 Problems

*This course prepares students for American Mathematics Competitions 10 and 12 and the non-proof parts of AIME. The topics taught include***the entire high school curriculum including trigonometry, advanced algebra, precalculus and advanced geometry,**but exclude calculus. Our curriculum also includes some additional challenging and brain-stimulating topics outside of the traditional school curriculum.**Recommended Grade Levels:**Although we do not limit students by grade level in our summer math camps, this course is typically recommended for advanced 7th and 8th graders and high school students.**Course Description:**This course will familiarize students with the essential concepts and techniques in Algebra II, PreCalculus, Combinatorics, Number Theory, and Geometry. We will have a specific emphasis on problem solving where the students will constantly be challenged to think creatively.**Contest Preparation:**AMC 10/12, AIME, ARML, Mandelbrot, Purple Comet.**Course Objectives:**As of the completion of the summer math camp, students will:1. Have complete mastery of concepts covered in standard Algebra II and PreCalculus courses, as well as more advanced topics (such as Vieta’s formulas, Complex Numbers, and manipulation of Series).

**Teaching Philosophy:**We believe that building good problem-solving skills is as (if not more) important than knowing lots of theorems. As such, although the course will cover a considerable amount of material, the main emphasis will be on building problem-solving intuition and training students to think creatively when faced with classes of problems they’ve never seen before.**Class Participation:**Students are expected to actively participate in class. We will employ the Socrates method, which is a cooperative dialogue between the students and teacher to stimulate critical thinking. Students will also collaborate with classmates while solving challenging problems.**Curriculum:**The course curriculum is owned and copyright by CyberMath Academy. The class material is composed of unique blends of problems hand picked from prestigious competitions from around the globe, along with many historical problems and fascinating puzzles.**Topics Covered In This Course****Algebra**– Quadratics/Discriminants & Conic Sections

– System of Equations

– Polynomial Division

– Rational Root Theorem

– Fundamental Theorem of Algebra

– Vieta’s Formulas

– Sequences and Series

– Induction

– Radicals and Rationalizing Denominators

– Algebraic Factorizations

– Complex Numbers

– Inequalities

– Functions

– Exponents and Logarithms**Combinatorics**– Basic Counting: Constructive and Complimentary

– Sets, Bijections, and Logic

– Principle of Inclusion Exclusion

– Combinations and Permutations

– Pascal’s Triangle

– Binomial Theorem

– Combinatorial Identities

– Pigeonhole Principle

– Expected Value

– Stars & Bars

– Recursion

– Fibonacci Numbers**Number Theory**– Prime Factorization

– Divisibility Rules

– Euclidean Algorithm

– Diophantine Equations

– Bezout’s Identity

– Modular Arithmetic & Exponentiation

– Fermat’s Little Theorem

– Wilson’s Theorem

– Chinese Remainder Theorem

– Multiplicative Functions

– Euler’s Theorem**Geometry**– Congruent & Similar Triangles

– Special Parts of a Triangle

– Triangle Area Formulas

– Quadrilaterals

– Angles in Polygons

– Inscribed Angles in Circles

– Power of a Point

– Three-Dimensional Geometry

– Trigonometry for Right Triangles

– Unit Circle & Radians

– Trigonometric Identities

– Extended Law of Sines & Law of Cosines

– Polar Coordinates & Geometry of Complex Numbers**Click below to see sample lecture notes****AUTHORS****Justin Stevens:**Accelerated Math Program Coordinator

University of Alberta – jstevens@cybermath.academy – (909) 713-4398**Forest Kobayashi:**Curriculum Designer, Harvey Mudd College**Alex Toller:**Curriculum Designer

If you would like to get more information on AMC 8, 10, 12 and AIME competitions, please visit Mathematical Association of America’s American Mathematics Competitions (AMC) Page.

**2- Students who would like to go above and beyond school mathematics**

Courses to choose from:

– Proof Mathematics with AIME Problems

This course is a part of our Math Olympiad Program. You can find more information about our Math Olympiad Program below.

###### Math Olympiad Program Levels

To find out what course is best for you at our summer math camp, please look at the information below:

There are two tracks in this course:

**Proof Mathematics with AIME Problems**For students who can comfortably qualify for the

AIME and solve the first half of problems on the exam. These students might be

aiming to qualify for USA(J)MO and have a pleasant start on the olympiad.**USA(J)MO:**For students who can already comfortably qualify for USA(J)MO, and

are aiming to score highly on it.**First: Please determine your level below**(1) Starting out on AMC, trying to qualify for AIME

(2) Can solve 2 problems on AIME, hoping to solve 8

(3) Can solve 6+ problems on AIME, hoping to solve 13

(4) Can qualify for USA(J)MO, hoping to solve a problem or two

(5) Can solve one or two USA(J)MO problems and solve hard USAJMO or medium USAMO problems

(6) Aiming to solve the final P3 / P6 problems on USAMO

**Second:Learn about the tracks in our Math Olympiad Program**Our Math Olympiad Program has two tracks:

*Entry Level Math Olympiad Course with Computations (Advanced AIME with Proofs)** Prerequisites: 6+ on AIME

* Aiming for high AIME scores, and a couple problems on USA(J)MO

*Advanced Math Olympiad Course (USAJMO)** Prerequisites: consistently qualify for USA(J)MO

* Aiming to score 14+ on USAMO

**Third: Placement**– If you are in levels 1 or 2, you should sign up for our Advanced High School Math with AMC 10/12 Problems course. It covers AMC 10/12 and the non-proof problems on AIME.

– If you are in levels 3 or 4, you should sign up for our Advanced AIME with Proofs course.

– If you are in levels 5 or 6, you should sign up for our USA(J)MO course.

Have questions? E-mail our Math Olympiad Program Coordinator Evan Chen at echen@cybermath.academy

###### Math Olympiad Program Curriculum

There are two tracks in this program:

**Advanced AIME with Proofs:**For students who can comfortably qualify for the

AIME and solve the first half of problems on the exam. These students might be

aiming to qualify for USA(J)MO and have a pleasant start on the olympiad.**USA(J)MO:**For students who can already comfortably qualify for USA(J)MO, and

are aiming to score highly on it.These two tracks overlap in any given year. The curriculum runs in a three-year cycle.

**Contest preparation:**AIME, HMMT, USA(J)MO, IMO.**Curriculum:**The course operates on a three-year cycle, so students can repeat the course up to three times total, across both tracks. The summer math camp and year-round materials are disjoint.A detailed listing of topics covered appears below. Not all topics occur in all years. Most topics occur in multiple years, but they will have different examples and problems each time they appear over the three-year cycle.

Each iteration of the course contains several practice exams.

**1- Topics appearing only in Advanced AIME with Proofs****Algebra***Symmetric Polynomials.*Vieta’s formulas, Newton sums, fundamental theorem of elementary symmetric polynomials.*Logarithms.*Computational problems and equations involving logarithms.*Trig Equation.*Algebraic problems involving trig functions.*Intro Functional Equation.*Introduction to olympiad-style functional equations. Substitutions, injectivity and surjectivity, Cauchy’s functional equation.*Inequalities.*Introduction to olympiad-style inequalities. AM-GM and Cauchy-Schwarz.

**Combinatorics***Computations with Probability.*Random variables, expected value, linearity of expectation.*Enumeration.*Computational counting problems.- Monovariants and Invariants.
*Finite processes.*

*Computational Geometry.*AIME-style problems in Euclidean geometry.

Angle Chasing.*Trig in Geometry.**Elementary Geometry.*Angle chasing, power of a point, homothety.*Basics of Complex Numbers. Introduction to complex numbers in geometry.*

**Number theory***Computations with Modular Arithmetic.*Fermat, Wilson, Chinese Remainder theorem.*Diophantine Equations.*Introduction to olympiad-style Diophantine equations.*Chinese Remainder Theorem.*

**2- Topics appearing in both tracks****Algebra***Generating Functions.*Their uses in combinatorial sums.*Linear Recursions and Finite Differences.**Sums.*Swapping order of summation.*Polynomials.*Fundamental theorem of algebra, factorizations, roots.

**Combinatorics***Weights and Colorings.**Induction and Recursion.**Linearity of Expectation and Double-Counting.**Algorithms.*Combinatorial problems involving discrete-time processes.*Graph Theory.*Definitions and problems.*Ad-Hoc Constructions.**Problems on Rectangular Grids.*

**Geometry***Power of a Point.**Homothety**Common Congurations.*

**Number theory***Divisibility and Euclidean Algorithm.*Bounding the remainders.*Look at the Exponent.*p-adic evaluation, lifting the exponent.*Orders. Primes of the form a2 + b2.*Primitive roots.

**3- Topics appearing only in USA(J)MO****Algebra***Functional Equations.*More diffi cult functional equations at the USAMO/IMO level.*Advanced Inequalities.*Jensen and Schur. Fudging, smoothing.*Analysis and Calculus.*Understanding the complete theorem statements in calculus and how they can be applied to olympiad problems. Differentiation and the relation

to multiplicity of roots. Lagrange multipliers. Compactness.

**Combinatorics***Advanced Graph Theory.*More di fficult olympiad problems involving graphs.*Advanced Algorithms.**Games and Processes.*

**Geometry***Projective Geometry.*Harmonic bundles, poles and polars.*Inversion.**Spiral Similarity.**Complex Numbers.*Applications to problems.*Barycentric Coordinates.*Applications to problems.

**Number theory***Constructions in Number Theory.**Integer Polynomials.*Irreducibility, minimal polynomials, a taste of Galois theory.*Quadratic Reciprocity.*Legendre symbols.

**Distribution of Math Strands**

**Morning Sessions:** Combinatorics and Geometry topics will be covered.

**Afternoon Sessions:** Algebra and Number Theory topics will be covered.

**Outstanding Teachers!**

Please see our faculty page for our instructors. Summer Math Camp instructors will be some of the instructors listed on our faculty page or other outstanding teachers with similar credentials.

**Schedule of Activities**

Date | Morning | Afternoon |
---|---|---|

Sun, July 14 | Residential and Int. Students Arrive | Orientation |

Mon, July 15 | Opening,Placement Tests & Guest Lecture | Math Classes |

Tue, July 16 | Math Classes | Math Classes |

Wed, July 17 | Math Classes | Math Classes |

Thu, July 18 | Math Classes | Math Classes |

Fri, July 19 | Math Classes | Math Classes |

Sat, July 20 | Math Classes | Math Classes |

Sun, July 21 | San Francisco Tour*** | San Francisco Tour*** |

Mon, July 22 | Math Classes | Math Classes |

Tue, July 23 | Math Classes | Math Classes |

Wed, July 24 | Math Classes | Math Classes |

Thu, July 25 | Math Classes | Math Classes |

Fri, July 26 | Math Classes | Math Classes |

Sat, July 27 | Practice Test | Award Ceremony, Stanford Campus Tour |

Sun, July 28 | Domestic Residential Students Depart | Academic Counseling, Study Planning |

Mon, July 29 | International Students Depart |

* For residential students. Day students can join with a $100 fee.

**Optional Additional Silicon Valley Trip**

Our San Francisco and Silicon Valley program offers eye-opening experiences and first hand exposure to the Silicon Valley’s top Hi Tech companies, its vibrant startup culture and exploration of the world renowned natural beauties of San Francisco Bay Area. Our students will have a detailed Stanford Campus Tour, which will include admissions information in addition to going atop the Hoover Tower and visiting Stanford’s state-of-the-art Bio-X Clark Center at which cutting edge interdisciplinary research takes place. We will also have a UC Berkeley Tour, the top public university in the U.S. After visiting Apple’s world-famous spaceship campus and the Apple Store on Infinite Loop, we will visit Google’s campus, see its unorthodox work environment and chat with ultra-smart Silicon Valley engineers. We will see how silicon becomes 0s and 1s at the Computer History Museum. How about the startups, incubators and coworking spaces? we will visit those too and see what’s brewing in Silicon Valley these days.

Natural Beauties? We will also see the beautiful San Francisco Bay Area. Our extended San Francisco tour includes a San Francisco Bay Area Boat Tour, Alcatraz, Sausolito, Muir Woods, Point Bonita and Mount Tamalpais to see the Bay Area from bird-eye view.

Please note that this is an optional program in addition to our regular summer camp program and requires an additional fee of $3,850. This fee covers everything including transportation, meals, accommodation, applicable entrance fees for museums and other attractions.

Date | Morning | Afternoon |
---|---|---|

Sun, July 28 | Extended SF Tour | Extended SF Tour |

Mon, July 29 | Stanford Admissions Information | Stanford Bio-X Clark Center Tour |

Tue, July 30 | Apple Spaceship Campus, Computer History Museum | Google Tour |

Wed, July 31 | Start Up Seminar, Incubator Tour | Engineers’ Forum |

Thu, August 1 | UC Berkeley Campus Tour | UC Berkeley Engineering Dept. Tour |

Fri, August 2 | Shopping Mall: SF Outlets | Students Depart |

**Daily Schedule**

Time | Activity | Notes |
---|---|---|

7:15 am – 8:15 am | Breakfast | Residential Students Only |

8:15 am – 8:45 am | Day students arrive | |

9:00 am – 12:15 pm | Morning classes | |

12:15 pm – 1:15 pm | Lunch and Activity time | Conversation with teachers/counselors |

1:15 pm – 4:30 pm | Afternoon classes | |

4:30 pm – 5:00 pm | Day students depart | |

5:00 pm – 6:00 pm | Free time | Residential Students Only* |

6:00 pm – 7:15 pm | Dinner | Residential Students Only* |

7:30 pm – 9:30 pm | Study Time | Residential Students Only* |

9:30 pm – 10:30 pm | Free Time | Residential Students Only |

10:45 pm | Lights Out | Residential Students Only |

*Day students who wish to attend supervised evening recreational and academic activities at the residential program may do so for an additional fee. The cost will be $200 (including dinner and all activities).

**Transportation to Summer Math Camp**

**Bus Service for Day Students**

We offer bus transportation to our camp site if enough number of students sign up for our Summer Math Camp as day students from the cities listed below. Extra charge will apply and space is limited.

For day students, we provide buses from the following cities: Cupertino, Sunnyvale, Mountain View and Fremont.

**Airport Pickup**

Domestic residential and international students who will be staying with us overnight at our summer math camp are expected to arrive at a San Francisco Bay Area airport (San Francisco, San Jose or Oakland) or at the camp site between 7 am – 7 pm on July 14th. For tuition and fees, please see below.

**Summer Math Camp Tuition and Deadlines**

Tuition Type | Deadline | Day Student | Residential Student |
---|---|---|---|

Super Early Bird | November 1st | $1,650 | $3,910 |

Early Registration | April 1st | $1,885 | $4,450 |

Regular Registration | June 1st | $1,985 | $4,700 |

Late Registration | July 14th | $2,085 | $4,950 |

Residential Tuition covers classes & teaching materials, activities, accommodation, meals and in-camp transportation.

**Fees**

International Students’ Fee: Additional $585.

Airport Pickup/Dropoff fee: $60 each

Lunch Fee for Day Students: $232 (Day Students might choose to bring their own lunch or purchase lunch at the University.)

Optional East Coast / Silicon Valley Program Fee: $3,850

**You can save up to $790 by registering early!**

**Admissions and Placement**

Please fill out the form below to apply. Please provide as much detailed information on the student’s background as possible:

**Background Information (not required for returning students):** Please provide the student’s background. Please include student’s academic achievements, GPA, any Honors or AP Courses taken, competition experience, any year-round or summer advanced courses/camps that the student has participated in.

We will get back to you with an admission decision and payment details if the student is admitted. All students will take a placement test on the first instructional day of our summer camps and will be assigned to their appropriate groups. We continuously monitor our students’ progress throughout the camp and make adjustments to their assignments when necessary. If you would like to discuss your child’s placement, please do not hesitate to give us a call or email us at info@cybermath.academy

###### Summer Math Camp Application

* This event is not owned, controlled, supervised or sponsored by Harvard University or any of its schools or programs.